Course Objectives

These are the course objectives from the textbook (A Problem Solving Approach to Mathematics for Elementary School Teachers by Billstein, Libeskind, and Lott). There are additional objections not from the book, such as problem solving objectives and mental math objectives. (Note for Spring 2016: Objectives are being adjusted to match the 12th Edition of the textbook.)

All objectives will appear on homework, homework quizzes, and potentially* on exams (*to keep exams reasonable in length, there may be some objectives which will not appear on exams). SBA (Standards Based Assessment) Objectives will also appear on SBA quizzes.

Objectives from Chapter 3

The student will be able to:

Section

SBA Objectives

Additional Objectives & Explanation Objectives

3-2

S.1 Models for Addition and Subtraction – Demonstrate* addition using the

(a1) join sets model (using manipulatives) and

(a2) number-line model

and demonstrate subtraction using the

(s1) take-away model (using manipulatives),

(s2) comparison model (using manipulatives), and

(s3) number-line model.

A.1 Closure Property of Addition and of Multiplication – Determine if a set is closed under addition and under multiplication. 3-1 (#A5, B5) & 3-3 (#A2, B2)

3-3

S.2 Properties of Addition and Multiplication – Given a sentence, identify the property illustrated.

S.3 Addition and Subtraction Algorithms with Units – Perform addition and subtraction with units, when regrouping may be required.S.4 Model the Standard Algorithms for Base-Ten Addition and Subtraction – Demonstrate (using base-ten blocks) addition (using the join sets model*) and subtraction (using the take-away model*). *On the quizzes you need to know to join and take-away.)

A.6 Addition and Subtraction Algorithms – Use the standard algorithms for addition and subtraction and use the equal-additions algorithms for subtraction. (#A5, B5)

S.7 Prime Factorization and Number of Factors – Find the prime factorization of a number and use it to determine the number of factors the number has.

A.14 Primes and Composites – Determine if a number is prime or composite. (#A2, B2)A.15 Prime Factorization – Find the prime factorization of a number that is already partially factored. (#A6, 17, 20; B6, 17, 20)A.16 List Factors – List all the factors (divisors) of a number. (#HO1)

4-3

S.8 Greatest Common Factor – Find the GCF using prime factorization and find GCF using the Euclidean Algorithm.S.9 Least Common Multiple – Find the LCM using prime factorization and find the LCM using the relationship between LCM and GCF. (Calculator allowed on standard 8 and 9.)

Objectives from Chapter 6

The student will be able to:

Section

SBA Objectives

Additional Objectives & Explanation Objectives

6-1

†

*E.1 Fundamental Law of Fractions – For any fraction and any number , E.2 Cross Multiplication for a Proportion – If , with , then .A.20 Model Fractions – State the fraction for a given diagram. (#A2-6; B2; Connections 7)A.21 Convert Units and Use a Scale – Solve problems involving scales and units. (#A21, B21)A.22 Problem Solving with Fractions – Apply fraction concepts to solve problems. (#A25, B14, 23; Connections TIMSS and NAEP items)

*E objectives are “Explanation” Objectives. These will be on a quiz late in the semester. For each objective, typically, you will be asked to explain:

Why we do it

Why it is legal

†For Chapters 6 and 7 we will not have PBA Quizzes, but instead will have Mastery Quizzes. There are 16 objectives on fractions, decimals, and percents. This are here.

Fraction-Decimal-Percent Objectives (from Chapter 6 and 7)

The student should be able to (by hand, without using a calculator):

1. Put a fraction into lowest terms.
2. Put a fraction into higher terms.
3. Rewrite an improper fraction as a mixed number.
4. Rewrite a mixed number as an improper fraction.
5. Add and subtract fractions (and mixed numbers).
6. Add and subtract decimals
7. Read a decimal number properly. (2.03 is “two and three hundredths”)
8. Convert fractions (and mixed numbers) to decimals and to percents.
9. Convert decimals to fractions (or mixed numbers) and to percents.
10. Convert percents to decimals and to fractions (or mixed numbers).
11. Multiply fractions (and mixed numbers).
12. Multiply decimals.
13. Divide fractions (and mixed numbers).
14. Divide decimals.
15. Solve percent problems of the form ___% of ___ is ___, where two of the three blanks are known and one of the blanks is unknown.
16. In a percent change situation, find the percent change, the amount of change, or the original amount.

Objectives from Chapter 7

The student will be able to:

Section

SBA Objectives

Additional Objectives & Explanation Objectives

7-1

†

A.31 Reading Decimals – Be able to read a decimal correctly. (#A4, B4)A.32 Expanded Place Value Form – Write a decimal in expanded place value form. (#A1, 2; B1, 2)A.33 Order Decimals – Put decimals in order (for example, from largest to smallest). (#A10, B10)

7-2

†

E.7 Adding and Subtracting Decimals – Explain why, when adding or subtracting decimals, we need to line up the decimals.E.8 Multiplying Decimals – Explain why, when multiplying decimals, we do not need to line up the decimals, but we count the number of decimals places to the right of the decimal points.E.9 Dividing Decimals – Explain why, you can, and should, move the decimal point in the divisor and the dividend to make the divisor a whole number.A.34 Problem Solving with Decimals – Apply concepts to solve problems involving decimals. (#A1-8; B1-8)

S.12 Geometric Patterns Given a geometric pattern, which produces a numeric pattern, find numbers in the sequence and the algebraic expression for the nth number in the sequence.

8-5

S.13 Multi-step Equations Solve multi-step equations.

A.39 Systems of Equations Solve a system of equations using substitution or elimination.A.40 Word Problems Resulting in a Systems of Equations Solve word problems involving systems of equations (using substitution or elimination).

“S.14” has been removed.

Objectives from Chapter 11

The student will be able to:

Section

SBA Objectives

Additional Objectives & Explanation Objectives

11-1

S.15 Intersections and Unions Find the intersection and union of points, lines, planes, segments, and rays.S.16 Relationship of Lines Determine if two given lines are skew, parallel, intersecting, or the same line.

A.41 Basic Notions Answer questions about the relationships of points, lines, planes, segments, and rays.A.42 Relationship of Planes Determine if two given planes are parallel, intersecting, or the same plane.A.43 Drawing Geometric Figures Draw geometric figures (a specific list will be provided in class).

A.44 Diagonals of a Polygon Determine the number of diagonals of an n-gon.A.45 Categorize Triangles Categorize triangles.A.46 Categorize Quadrilaterals Categorize quadrilaterals.

11-3

S.18 Angles in a Polygon Solve problems involving the angles in an n-gon (which may, or may not, be regular).

A.47 Angles Formed by Parallels Apply relationships of angles formed by parallel lines and transversals (to find angles or determine if the lines are parallel).E.10 180° in a Triangle – Show why there are 180° in a triangle, three different ways.

11-4

S.19 Find the number of vertices, edges, and faces Given a description or picture of a pyramid, prism, or Platonic solid, determine the number of vertices, edges, and faces.